Interactive Pen-and-Ink Rendering for Implicit Surfaces

Ryan Schmidt∗

University of CalgaryTobias Isenberg∗

University of CalgaryBrian Wyvill∗

University of Calgary

(a) (b) (c) (d) (e)

Figure 1: An implicit surface model visualized using a smooth-shaded triangle mesh (a) and a pen-and-ink drawing (b). The generatedsilhouettes (d) are much smoother than base mesh (c) and render at interactive rates. Suggestive contours (e) add important additional detail.

1 Introduction

The shape of a complex surface can often be conveyed with just“a few good lines”. Line rendering is particularly beneficial whenvisualizing implicit surfaces, as the cost of extracting sufficientlyaccurate iso-surfaces can be very high. We are exploring the use oflow-resolution iso-surface meshes generated in real-time [Schmidtet al. 2005] to interactively render implicit surfaces in a pen-and-ink style. Our approach utilizes silhouettes and feature contoursextracted from coarse meshes as an initial approximation to the ac-tual surface contours. These coarse feature lines are then iterativelyrefined using the implicit functions, producing smooth and highlyinteractive results.

Rapid visualization is critical in interactive modeling systems,where designers require real-time feedback as they manipulateand deform the implicit surface. Recent pen-and-ink approachesfor functional implicit surfaces [Foster et al. 2005] generate high-quality but time-consuming results. The relatively high cost of im-plicit function evaluation prohibits interactive volume dataset gen-eration, ruling out related methods [Burns et al. 2005]. Our ap-proach, while demonstrated using implicit surfaces, is applicableto any functional smooth surface, including NURBS surfaces. Therenderer is used for interactive visualization in a sketch-based mod-eling system, where it has particular aesthetic value.

2 Dynamic Silhouette Refinement

We begin with a coarse base mesh (Fig. 2(a)). Silhouettes are ex-tracted using standard brute-force sub-polygon methods. Accuratesurface normals and curvatures are computed from the implicit func-tion, not the mesh. The silhouette loops are then projected onto thesurface (Fig. 2(b)). On implicit surfaces this is done using a fewsteps of gradient descent, on NURBS patches the surface pointscan be directly evaluated. Then, the linear silhouette segments arerepeatedly subdivided and projected onto the surface until an errorthreshold is reached (Fig. 2(c)).

Our algorithm gives very good results for regular silhouettes(N ·V = 0; see Fig. 1). The iterative refinement converges to the cor-rect silhouette under relatively weak conditions on the base mesh

∗{rms | isenberg |blob}@cpsc.ucalgary.ca

and implicit function. We have also experimented with sugges-tive contours (radial curvature kr = 0), using a finite-difference ap-proach which does not require third derivatives. Mesh resolutionappears to have more effect on suggestive contours, although wehave not carefully tuned the various available parameters.

Hidden-line removal presents a challenge, as implicit surface ray-intersection is too slow. The coarse mesh can be used, howeverfeature lines will be erroneously clipped in areas of negative curva-ture. Instead, we again utilize the base mesh. Points are distributedon each triangle and projected to the surface. A small tangent discis rendered into the z-buffer at each point, providing fast and rea-sonably accurate hidden-line removal. In addition, these discs canbe used to efficiently render stippling points (Fig. 1(b), 2(d)).

The base mesh also provides an efficient means for hierarchi-cally organizing data, simplifying dynamic generation and visibil-ity culling. As a result there is little unnecessary pre-computationoverhead, which improves response time during surface deforma-tion. 15–30 fps are achieved for static manipulation of moderately-complex stippled models, and 1–5 fps during interactive editing.

(a) (b) (c) (d)

Figure 2: Silhouette projection from the base mesh to the implicitsurface, silhouette subdivision, and final result with stippling.

References

BURNS, M., KLAWE, J., RUSINKIEWICZ, S., FINKELSTEIN, A.,AND DECARLO, D. 2005. Line Drawings from Volume Data.ACM Transactions on Graphics 24, 3 (July), 512–518.

FOSTER, K., JEPP, P., WYVILL, B., SOUSA, M. C., GALBRAITH,C., AND JORGE, J. A. 2005. Pen-and-Ink for BlobTree ImplicitModels. Computer Graphics Forum 24, 3 (Sept.), 267–276.

SCHMIDT, R., WYVILL, B., AND GALIN, E. 2005. InteractiveImplicit Modeling with Hierarchical Spatial Caching. In Proc.of Shape Modeling International, IEEE Inc., 104–113.

http://www.unknownroad.com/http://www.ucalgary.ca/http://cpsc.ucalgary.ca/~isenberg/http://www.ucalgary.ca/http://cpsc.ucalgary.ca/~blob/http://www.ucalgary.ca/mailto:rms@cpsc.ucalgary.camailto:isenberg@cpsc.ucalgary.camailto:blob@cpsc.ucalgary.camailto:rms@cpsc.ucalgary.cahttp://doi.acm.org/10.1145/1073204.1073222http://dx.doi.org/10.1111/j.1467-8659.2005.00851.xhttp://dx.doi.org/10.1111/j.1467-8659.2005.00851.xhttp://dx.doi.org/10.1109/SMI.2005.25http://dx.doi.org/10.1109/SMI.2005.25

Interactive Pen-and-Ink Rendering for Implicit Surfaces– Additional Figures –

Ryan Schmidt∗

University of CalgaryTobias Isenberg∗

University of CalgaryBrian Wyvill∗

University of Calgary

(a) (b) (c)

(d) (e) (f)

Figure 3: Silhouette example on a low-resolution mesh of a simple implicit surface. A low-resolution base mesh is shown in (a), the smoothsilhouette extracted using our method is shown in (b). The silhouette is nearly identical to the high-resolution silhouette in (c), as shown in thedifference image (d). For comparison, the low-resolution mesh silhouette is shown in (e), and the low-resolution silhouette after projectionbut before subdivision is shown in (f). The projection step alone clearly provides a significant improvement in silhouette quality, howeversubdivision is necessary to impart a real sense of smoothness (b).

(a) (b) (c)

Figure 4: An extreme example of our silhouette refinement algorithm. The base mesh in (b) is a very low-resolution polygonization of theshape in (a). However, the silhouette (c) from this low-resolution base mesh, once projected and refined, is still quite accurate.

∗{rms | isenberg |blob}@cpsc.ucalgary.ca

http://www.unknownroad.com/http://www.ucalgary.ca/http://cpsc.ucalgary.ca/~isenberg/http://www.ucalgary.ca/http://cpsc.ucalgary.ca/~blob/http://www.ucalgary.ca/mailto:rms@cpsc.ucalgary.camailto:isenberg@cpsc.ucalgary.camailto:blob@cpsc.ucalgary.camailto:rms@cpsc.ucalgary.ca

(a) (b) (c) (d)

Figure 5: Implicit surface with relatively fine details: (a) Gouraud-shaded and (b) wireframe images of the implicit surface’s low-res basemesh, (c) base mesh with silhouette, and (d) silhouette only.

(a) (b) (c) (d)

Figure 6: Even high-resolution iso-surface polygonization can lead to poor-quality representation of finer details (a). Silhouette refinement(b) improves the representation of small details such as the toes. Suggestive contours (c) and stippling (d) improve perception of surfacedetail.

(a) (b) (c)

Figure 7: Complex model rendered using our technique with silhouettes and suggestive contours (a) as well as with additional stippling (b).A different view of the model with silhouette lines, suggestive contours, and stippling is shown in (c).

IntroductionDynamic Silhouette Refinement